[sdiy] Uniformly distributed noise generator?

[Magnus Danielson]

On 06/10/2013 01:55 PM, Steven Cook wrote:
> Hi,
>
>> gaussian (like normal noise circuits)
>
> Maybe I've not had enough coffee today, but isn't ordinary white noise
> uniformly distributed rather than gaussian?

Get your coffee. White noise is gaussian.

A little exercise:

Take one uniformly distributed noise source, look at it's distribution 
and you will find it to be uniform.

Now, add a second uniform distributed noise source (of the same 
amplitude), now look at the distribution and you will find that it is in 
fact not uniform anymore, it is triangular. If you subtract the two 
noises, it will sit neatly around zero (many is normalized between 0 and 1).

Now, build another pair and add, and you start getting somewhat bell-shaped.

As you have taken six pairs, you have a pretty gaussian shaped 
distribution, and it has the RMS value of 1.

As you now add more and more pairs you get a more perfect gaussian 
distribution bell, and as you go for infinitly many, you get the 
gaussian distribution with all it's properties, such as infinite 
peak-to-peak value.

As you look at the spectrum analyzer, it will be flat, and as you 
integrate over longer and longer time, it will be flatter and flatter.

This trick to build gaussian distribution out of a uniform distribution 
is a common trick, if one does not use the Box-Muller approximation 
which is another way to do it. The use of 12 noise samples is very 
common, as it's RMS value becomes unity, but with some simple scaling 
other numbers can be used to achieve the wanted RMS scaling accurately.

Actually adding sines with it's quirky distribution resists this harder, 
but after sufficient numbers it also goes gaussian.

Sorry for making some noise.

Cheers,
Magnus